The appeal included arguments that Eaglin's attorneys should have raised issues about his diagnosis of bipolar disorder and about abuse he suffered as a child.

But the Supreme Court pointed to what are known as "aggravators," which are factors considered in determining whether murder defendants should receive the death penalty.

"Even if counsel had presented testimony during the penalty phase that shed light on Eaglin's abusive childhood, his dysfunctional family, and that he suffered from mental health disorders, our confidence in the outcome of the penalty phase would not be undermined when viewed in the context of the penalty phase evidence and the mitigators and aggravators found by the trial court,'' the Supreme Court opinion said.